1. Field of the Invention
The invention relates especially to a method for the learned or blind identification of a number of sources P that is potentially greater than or equal to the number N of sensors of the reception antenna.
It can be used for example in the context of narrow-band multiple transmission.
It is used for example in a communications network.
It can be applied especially in the field of radio communications, space telecommunications or passive listening to these links in frequencies ranging for example from VLF to EHF.
FIG. 1 is a schematic drawing exemplifying an array of several reception sensors or receivers, each sensor receiving signals from one or more radio communications transmitters from different directions of arrival
Each sensor receives signals from a source with a phase and amplitude that are dependent on the angle of incidence of the source and the position of the sensor. FIG. 2 is a drawing exemplifying the parameterization of the direction of a source. This direction is parameterized by two angles corresponding to the azimuth angle θ and the elevation angle Δ.
2. Description of the Prior Art
The past 15 years or so have seen the development of many techniques for the blind identification of signatures or source direction vectors, assumed to be statistically independent. These techniques have been developed in assuming a number of sources P smaller than or equal to the number of sensors N. These techniques have been described in the references [1][3][7] cited at the end of the description. However, for many practical applications such as HF radio communications, the number of sources from which signals are received by the sensors is increasing especially with the bandwidth of the receivers, and the number of sources P can therefore be greater than the number of sensors N. The mixtures associated with the sources are then said to be under-determined.
A certain number of methods for the blind identification of under-determined mixtures of narrow-band sources for networks have been developed very recently and are described in the references [2] [7-8] and [10]. The methods proposed in the references [2] and [7-8] make use of information contained in the fourth-order (OF) statistics of the signals received at the sensors while the method proposed in the reference [10] make use of the information contained in one of the characteristic functions of the signals received. However, these methods have severe limitations in terms of the prospects of their operational implementation. Indeed, the method described in the reference [2] is very difficult to implement and does not provide for the identification of the sources having the same kurtosis values (standardized fourth-order cumulant). The methods described in the references [7-8] assume that the sources are non-circular. These methods give unreliable results in practice. Finally, the reference method [10] has been developed solely for mixtures of sources with real (non-complex) values.
The object of the present invention relates especially to a new method for the blind identification of an under-determined mixture of narrow-band sources for communications networks. The method can be used especially to identify up to N2−N+1 sources from N identical sensors and up to N22 sources with N different sensors, in assuming only that the sources have different tri-spectra and non-zero, same-sign kurtosis values (this hypothesis is practically always verified in the context of radio communications).